Question

a pendant is formed using a cylinder and cone. once assembled, as shown below, the pendant is painted. how many square millimeters are covered with paint? express the answer in terms of π. 336π square millimeters 400π square millimeters 416π square millimeters 464π square millimeters

Explanation:

Step1: Calculate cone lateral - area

The formula for the lateral - area of a cone is $A_{cone}=\pi rl$, where $r = 8$ mm and $l = 10$ mm. So $A_{cone}=\pi\times8\times10 = 80\pi$ square millimeters.

Step2: Calculate cylinder lateral - area

The formula for the lateral - area of a cylinder is $A_{cylinder}=2\pi rh$, where $r = 8$ mm and $h = 12$ mm. So $A_{cylinder}=2\pi\times8\times12=192\pi$ square millimeters.

Step3: Calculate base - area of cylinder

The formula for the area of a circle (base of the cylinder) is $A_{base}=\pi r^{2}$, where $r = 8$ mm. So $A_{base}=\pi\times8^{2}=64\pi$ square millimeters.

Step4: Calculate total painted area

The total area to be painted is the sum of the cone's lateral area, the cylinder's lateral area, and the cylinder's base area. $A = A_{cone}+A_{cylinder}+A_{base}=80\pi + 192\pi+160\pi=416\pi$ square millimeters.

Answer:

C. $416\pi$ square millimeters